The quotient of 6 and 2, times 3, plus the difference of 18 and 5?

Given the function D(x) is defined as shown in the table

Part 1: Find D(0)

So, from the table, we will choose the value of D when x = 0

So,

Part 2: Evaluate D(5)

We will choose the value of D when x = 5

Part 3: Determine D(0) - D(5)

So, we will subtract the values of part1 and part2

Answer:

108 m^3

Step-by-step explanation:

The volume of a rectangular prism is the product of all its sides. 12 * 6 * 1.5 = 108

The value of such that = k * 180, where k is an integer, is the value at which cotangent is undefinable.

Cotangent, or cot, is one of the six standard trigonometric functions. Cotangent of an angle is defined as the ratio of the adjacent side to the opposite side of a right-angled triangle.

The value of cotangent is undefined when the denominator is zero. This implies that cotangent is undefined at angles where the value of sine is zero.

Since the sine function is periodic and has a period of 360 degrees, the values of sine repeat themselves after every 360 degrees.

For this reason, cotangent is undefined at angles such that θ = k * 180, where k is an integer.

That is, cotangent is undefined at 0°, 180°, 360°, and so on. It is also important to note that cotangent is a periodic function, and its values repeat every 180 degrees.

Therefore, cotangent is undefined at 0° + k * 180°, where k is an integer.

To summarize, the value of Θ at which cotangent is undefined is such that θ = k * 180, where k is an integer.

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Check the picture below.

\(\textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{h}{\sin(157^o)}=\cfrac{240}{\sin(6^o)}\implies h\sin(6^o)=240\sin(157^o) \\\\\\ h=\cfrac{240\sin(157^o)}{\sin(6^o)}\implies h\approx 897.1~cm\)

Make sure your calculator is in Degree mode.

The amοunt οf space within the cylinder that is nοt taken up by the tennis balls is abοut 12.56 cubic inches.

A cylinder is a three-dimensiοnal geοmetric shape that cοnsists οf twο parallel circular bases οf the same size and shape, and a curved lateral surface cοnnecting the bases.

The vοlume οf the cylindrical cοntainer can be calculated using the fοrmula fοr the vοlume οf a cylinder:

Vcylinder = πr²h

where the cylinder's radius (r) and height (h) are given.

Substituting the given values, we have:

Vcylinder = 3.14 x 1² x 8Vcylinder = 25.12 cubic inches

The vοlume οf οne tennis ball can be calculated using the fοrmula fοr the vοlume οf a sphere:

Vball = 4/3 x πr³

where r is the radius οf the tennis ball.

Substituting the given value, we have:

Vball = 4/3 x 3.14 x 1³

Vball = 4.19 cubic inches

Since there are three tennis balls, the tοtal vοlume they take up is:

3 x Vball = 3 x 4.19 = 12.57 cubic inches.

Therefοre, the amοunt οf space within the cylinder that is nοt taken up by the tennis balls is:

Vcylinder - 3 x Vball = 25.12 - 12.57 = 12.55 cubic inches

Rοunding this answer tο the nearest hundredth gives:

12.55 rοunded tο the nearest hundredth is 12.56 cubic inches.

Hence, the amοunt οf space within the cylinder that is nοt taken up by the tennis balls is abοut 12.56 cubic inches.

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Answer:

Last answer

Step-by-step explanation:

Interest is a fee charged by a lender to a borrower for the use of money or credit, usually expressed as a percentage of the amount borrowed or invested over a period of time. Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.  The total interest earned after one year is $229

How much was in each account?

Let x be the amount invested in the first account that pays 3% interest, and let y be the amount invested in the second account that pays 8% interest. Since the total amount invested is $5800, we have:

\(x + y = 5800\)

The amount of interest earned on the first account is 0.03x, and the amount of interest earned on the second account is 0.08y. Since the total interest earned after one year is $229, we have:

\(0.03x + 0.08y = 229\)

We now have two equations with two unknowns:

\(x + y = 5800\)

\(0.03x + 0.08y = 229\)

We can solve for x and y by using elimination or substitution method. Here, we will use the substitution method.

Solve the first equation for x:

\(x = 5800 - y\)

Substitute this expression for x into the second equation and solve for y:

\(0.03(5800 - y) + 0.08y = 229\)

\(174 - 0.03y + 0.08y = 229\)

\(0.05y = 55\)

\(y = 1100\)

Now substitute this value of y into either equation to solve for x:

\(x + 1100 = 5800\)

\(x = 4700\)

Therefore, Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.

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Intersection points for the lines are,

⇒ (3, 5) (1, 7) and (1, 5)

Line segment is the part of line which have two endpoint and bounded by two distinct end points and it contain every point on the line which is between its endpoint.

Given that;

The equation of lines are,

x + y = 8  .. (i)

y = 5 .. (ii)

x = 1  .. (iii)

Now, Intersect point for equation (i) and (ii);

x + y = 8  .. (i)

y = 5 .. (ii)

⇒ x + 5 = 8

⇒ x = 3

Hence, The intersection point = (3, 5)

And, Intersect point for equation (i) and (iii);

x + y = 8  .. (i)

x = 1  .. (iii)

⇒ x + y = 8

⇒ y = 8 - 1

⇒ y = 7

Hence, The intersection point = (1, 7)

And, Intersect point for equation (ii) and (iii);

⇒ (1, 5)

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Answer:

{ 100, 125,150,175}

Step-by-step explanation:

The range  is the output values

{ 100, 125,150,175}

First: Plot a point at (-5,-2).

Then, from that point at (-5,-2), count "up 1 and right 3" to plot a second point.  (This is based on the slope being 1/3.)

You can then either repeat that for a third point or just draw the line at that point between those two points.

Remember that slope is "rise over run".

Answers

This picture contains the right answers

Applying the law of exponents, the expressions that are equivalent to x^3/8 are:

B. \(\sqrt[8]{x^3}\)

D. \((\sqrt[8]{x})^3\)

One of the law of exponents is given as: \(x^{\frac{m}{n} } = \sqrt[n]{x^m}\).

Thus, given the expression, x^3/8

Applying the law of exponent, we have:

\(x^{\frac{3}{8} } = \sqrt[8]{x^3} = (\sqrt[8]{x})^3\)

Therefore, applying the law of exponents, the expressions that are equivalent to x^3/8 are:

B. \(\sqrt[8]{x^3}\)

D. \((\sqrt[8]{x})^3\)

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According to the information, we can infer that Mazibane must pay R3640 into the account on 30 June to have no debt.

To calculate the amount Mazibane must pay on 30 June to have no debt in the account, we need to consider the initial debt, the interest, and the previous payment.

Initial Debt:

Interest Calculation:

Previous Payment:

To determine the remaining debt on 1 June, we subtract the payment from the initial debt:

From 1 June to 30 June, a period of one month, interest is charged on the remaining debt.

To calculate the interest for one month, we use the formula:

where the principal is the remaining debt, the rate is the monthly interest rate (16%/12), and the time is the number of months (1).

To find the total debt on 30 June, we add the remaining debt on 1 June and the interest for one month:

To have no debt on 30 June, Mazibane must pay the total debt amount:

Calculating the interest and summing up the values, we find that Mazibane must pay approximately R3640 into the account on 30 June to have no debt.

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Answer:

1.4

Step-by-step explanation:

hope it helped

Answer:

12 cubic cm

Step-by-step explanation:

\(V_{1\: cube} = \bigg( \frac{1}{2} \bigg )^{3} = \frac{1}{8} \: {cm}^{3} \\ \\ \implies \:V_{96\: cubes} = 96 \times \frac{1}{8} \: {cm}^{3} = 12\: {cm}^{3} \)

It is given that: prism is completely filled with 96 cubes.

\(\implies \: V_{prism} =V_{96\: cubes}\)

\(\implies \: \huge \red{V_{prism} = 12\: {cm}^{3}}\)

Answer:A.The triangles are similar but not congruent

Step-by-step explanation:

In a congruent traingle:

the both triangles are same in shape and size

There are five theorems to see if the triangles are congruent

and neither particularly applies here

sss: the sides are not equal

as none of the sides are equal, then despite the angles, congruence is not possible

However it is evident that one of the triangles is proportionally bigger than the other but similar. Hence A is correct.

Step-by-step explanation:

Answer:
V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Step-by-step explanation:

Set up the variables: Let V represent the number of vans, S represent the number of small trucks, and L represent the number of large trucks.

Write the equations:

V + S + L = 310 (total number of vehicles)

V = 2S (twice as many vans as small trucks)

35,000V + 70,000S + 60,000L = 15,000,000 (total cost of the vehicles)

Substitute equation 2) into equation 1):

2S + S + L = 310

3S + L = 310

Simplify equation 3) by substituting V = 2S:

70,000S + 70,000S + 60,000L = 15,000,000

140,000S + 60,000L = 15,000,000

Set up a system of equations:

3S + L = 310

140,000S + 60,000L = 15,000,000

Eliminate L by multiplying equation 1) by 60,000:

60,000(3S + L) = 60,000(310)

180,000S + 60,000L = 18,600,000

Subtract equation 2) from the new equation:

(180,000S + 60,000L) - (140,000S + 60,000L) = 18,600,000 - 15,000,000

40,000S = 3,600,000

Solve for S:

S = 90

Substitute the value of S into equation 1) to solve for L:

3(90) + L = 310

270 + L = 310

L = 40

Substitute the values of S and L into equation 2) to solve for V:

V = 2S

V = 2(90)

V = 180

The final answer is:

V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Answer:

180 Vans 90 Small trucks and 40 Large trucks

Step-by-step explanation:

Answer: 19.6

Step-by-step explanation:

5 odd numbers equal to 32 has no solutions.

An odd numbers is described as any  number that cannot be divided into two separate integers evenly.

The equation above will have no possible solutions because it does not follow with regards to parity.

odd + odd = even

even + even = even

even + odd = odd

In the case of  5 odd numbers,

odd + odd + odd + odd + odd

= even + even + odd

= even + odd

= odd

The above  will remain true irrespective of the numbers being either  positive or negative.

In conclusion, the answer in the equation provided to us is  32 which is an even number, hence no solution sets.

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The roots of the given polynomial using the rational zero theorem are;  2, -4 and 6.

We are given the polynomial;

y = x³ - 4x² - 20x + 48

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient (the coefficient of the constant term) is 48

Find its factors (with the plus sign and the minus sign): ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

These are the possible values for p.

The leading coefficient (the coefficient of the term with the highest degree) is 1.

These are the possible rational roots:

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

Checking the possible roots: if a is a root of the polynomial P(x), the remainder from the division of P(x) by x - a should equal 0 (according to the remainder theorem, this means that P(a)=0

Plugging in those values, the only ones that yield P(a) = 0 are; 2, -4 and 6.

Thus, these are the roots of the given polynomial.

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Answer:

An increase of $0.94

Step-by-step explanation:

The equation of each line that satisfies the given conditions are:

1. y - 2 = 5/2(x - 3)

2. y - 4 = m(x + 3)

3. y = -3x + 5

1. Given the points, (3, 2) and (5, 7), find the slope (m):

Slope (m) = change in y / change in x = (7 - 2)/(5 - 3)

m = 5/2

Write the equation in point-slope form by substituting m = 5/2 and (a, b) = (3, 2) into y - b = m(x - a):

y - 2 = 5/2(x - 3)

2. Given:

A point = (-3, 4)

Slope (m) = 2

Substitute (a, b) (-3, 4), and m = 2 into y - b = m(x - a):

y - 4 = m(x + 3) [equation of the line]

3. Given:

Slope (m) = -3

Y-intercept (b) = 5

Substitute m = -3 and b = 5 into the equation y = mx + b:

y = -3x + 5

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Answer:

35

Step-by-step explanation:

7 * 5 = 35

Answer:

x = 11

Step-by-step explanation:

3x+1 = 2x+12 (subtract 2x from both sides)

x+1 = 12 (subtract 1 from both sides)

x = 11

So x is equal to 11

The largest ratio, among the following ratios: 5/36, 2:9, 3 to 18, 1:3 is 1:3.

The ratio refers to the relative size of one quantity compared to another.

The ratio, which is the quotient of two quantities or values, can be expressed as a decimal, percentage, or fraction.  We can also express the ratio in its standard form (:).

Given   Sum of     Equivalent

Ratio     Ratios          Ratios

5/36        36         13.89% or 0.1389

2:9           11          18.18% or 0.1818

3 to 18     21          14.28% or 0.14.28

1:3            4           25% or 0.25

Thus, we can conclude that 1:3 is the largest ratio amont the others.

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The cost of each bottle is $\(1\)

Given:

To find: Cost of each bottle of juice?

It is given that Miguel bought snacks for his team's practice which includes a bag of popcorn, and \(20\) packs of juice bottles out of which the bag of popcorn cost him $\(3.33\) , and the total cost before tax of all the items costs him $\(23.33\)

Now we have to find that how much each bottle of juice costs him as asked in the given question.

Let the bag of popcorn's amount be x and the pack of bottle juice is y

Now according to the linear equation in two variable

\(x*1+y*20=23.33\)........(1)

where 1 is the total pack of popcorn bag and \(20\) the amount of bottle juice packs

As we know that \(x=3.33\) since a bag of popcorn costs him $\(3.33\)

Now put the value of x in (1) hence,

\(3.33*1+y*20=23.33\)

On further solving we get,

\(20y=20\)

On further solving we get,

\(y=1\) as the price of every juice of bottle.

Hence a bottle of juice costs him $\(1\)

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Answer:

\(Probability = 0.56\)

Step-by-step explanation:

Represent the probability that Alice does well with P(A), the probability that Bob does well with P(B).

So, we have:

\(P(A) = 0.8\)

\(P(B) = 0.4\)

Required

Determine the probability that only one of them do well

This event is represented as: (A and B') or (B and A')

Where B' means Bob does not perform well and A' means Alice does not perform well.

And:

\(P(B') = 1 - P(B)\)

\(P(A') = 1 - P(A)\)

So, the probability becomes:

\(Probability = P(A\ and\ B')\ or\ P(B\ and\ A')\)

\(Probability = P(A) * P(B')\ +\ P(B)*P(A')\)

\(Probability = P(A) * (1-P(B)) +\ P(B)*(1-P(A))\)

\(Probability = 0.8 * (1-0.4) +\ 0.4*(1-0.8)\)

\(Probability = 0.8 * 0.6 +\ 0.4*0.2\)

\(Probability = 0.48 + 0.08\)

\(Probability = 0.56\)

Hence, the required probability is 0.56

Answer:

12. 35 degrees

14. 110 degrees

Step-by-step explanation:

Since DE is equal to EF this triangle is and isosceles triangle. Which tells us that the base angle are equal. Therefore x is 35 degrees.

Triangle DMN is also an isosceles triangle because DM=MN. So, angle MND is 35 degrees. Angles in a triangle add up to 180 degrees so we can create the equation:

DMN+MDN+MND=180

2(35)+DMN=180

DMN=110

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